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Semi-matching algorithms for scheduling parallel tasks under resource constraints

Anne Benoit 1, 2 Johannes Langguth 2 Bora Uçar 1, 2, * 
* Corresponding author
1 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We study the problem of minimum makespan scheduling when tasks are restricted to subsets of the processors (resource constraints), and require either one or multiple distinct processors to be executed (parallel tasks). This problem is related to the minimum makespan scheduling problem on unrelated machines, as well as to the concurrent job shop problem, and it amounts to finding a semi-matching in bipartite graphs or hypergraphs. The problem is known to be NP-complete for bipartite graphs with general vertex (task) weights, and solvable in polynomial time for unweighted graphs %with unit weights (i.e., unit-weight tasks). We prove that the problem is NP-complete for hypergraphs even in the unweighted case. We design several greedy algorithms of low complexity to solve two versions of the problem, and assess their performance through a set of exhaustive simulations. Even though there is no approximation guarantee for these low-complexity algorithms, they return solutions close to the optimal (or a known lower bound) in average.
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Submitted on : Thursday, January 2, 2014 - 7:11:01 PM
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Anne Benoit, Johannes Langguth, Bora Uçar. Semi-matching algorithms for scheduling parallel tasks under resource constraints. IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum, May 2013, Cambridge, MA, United States. pp.1744-1753, ⟨10.1109/IPDPSW.2013.30⟩. ⟨hal-00738393v5⟩



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